### Upcoming Talks

#### Zahlentheoretisches Kolloquium

Title: Values of binary partition function represented by a sum of three squares
Speaker: Dr. Maciej Ulas (Jagiellonian University, Krakow)
Date: 07.02.2023, 11:00 Uhr
Room: Seminarraum Analysis-Zahlentheorie, Kopernikusgasse 24, 2.OG
Abstract:

Let $m$ be a positive integer and $b_{m}(n)$ be the number of partitions of $n$ with parts being powers of 2, where each part can take $m$ colors. We show that if $m=2^{k}-1$, then there exists the natural density of integers $n$ such that $b_{m}(n)$ can not be represented as a sum of three squares and it is equal to $1/12$ for $k=1, 2$ and $1/6$ for $k\geq 3$. In particular, for $m=1$ the equation $b_{1}(n)=x^2+y^2+z^2$ has a solution in integers if and only if $n$ is not of the form $2^{2k+2}(8s+2t_{s}+3)+i$ for $i=0, 1$ and $k, s$ are non-negative integers, and where $t_{n}$ is the $n$th term in the Prouhet-Thue-Morse sequence. A similar characterization is obtained for the solutions in $n$ of the equation $b_{2^k-1}(n)=x^2+y^2+z^2$. This talk is based on a joint work with Bartosz Sobolewski (Jagiellonian University).

#### Vortrag im Rahmen des Seminars Applied Analysis and Computational Mathematics

Title: An adaptive least squares boundary element method for elliptic boundary value problems
Speaker: Univ.-Prof. Dr. Olaf Steinbach (Institut für Angewandte Mathematik, TU Graz)
Date: Montag, 6.2.2023, 10:00 Uhr
Room: Seminarraum AE02, Steyrergasse 30, EG
Abstract:

#### Vortrag im Rahmen des Seminars Applied Analysis and Computational Mathematics

Title: Stability of space-time boundary element methods for 1D wave problems
Speaker: Daniel Hoonhout (TU Delft)
Date: Montag, 6.2.2023, 9:00 Uhr
Room: Seminarraum AE02, Steyrergasse 30, EG
Abstract: